If you are buying a bike, there are a lot of different speeds. Is there a complete list of speeds? I'm trying to create an array...
var allSpeeds = ["single-speed","3-speed","12-speed"];
While not everything is commonly available new now, every number from 1 to 33 has been found on new bikes except 13, 17, 19, 23, 25, 26, 28, 29, 31, and 32. If you start counting quad chainring setups and internal hubs with clusters hacked on to them you get access to a bunch of other weird numbers.
Note that looking at the number of speeds itself is basically trivia. The gearing range and the interval between available gears tell an equally or more important part of the story.
The number of 'speeds' a bicycle is quoted as having is really the number of gear ratios available. There is no definitive list.
On a single speed bike this is, by definition, 1.
On a internal hub geared bike the minimum number is usually 3, maximum I've heard of is
On a derailleur equipped bike the number of ration is usually said to be the number of sprockets on the rear wheel multiplied by the number of sprockets on the crank, hence the classic '10 speed' with 5 rear and 2 crank sprockets. Bikes that have more than 1 front sprocket have significant overlap between ration available in each, so the effective number of ratios is actually less.
In recent times less expensive bikes tend to have 6, 7, 8 or 9 rear sprockets combined with 3 crank sprockets. Road bikes have 9, 10 or 11 rear x 2 front. A recent development is 11 or 12 rear and a single front sprocket on mountain bikes and some road bikes.
You can see that there are many gear ratio choices. The only hard rule is that derailleur bikes with more that one crank sprocket cannot have a number of ratios that is a prime number (3, 5, 7, 11, etc.)
The "meaning" of gear "speeds" is different depending upon the type of gear system:
"Single speed" is clear. There are no variable gears. You will travel the same distance for each revolution of the cranks, which the pedals are attached to. If you pedal faster, you will go faster. If you pedal slower you will go slower. A special case of "single speed" is "fixed gear", where you can't freewheel. If the bike is moving, so are the pedals.
Bike with "hub gears". Also known as IGH (internal gear hubs). Examples include Shimano Alfine, Shimano Nexus, Sturmey Archer, Rohloff. All the mechanism is contained within the rear hub. You change gear to change the RATIO between how fast you pedal and how fast the bike goes. So going up a hill you will change to a "low" gear. You will pedal at the same speed as you were pedalling on the flat, but the bike will go up the hill slower. If you couldn't change gear you would have to pedal very slowly, and with a lot of effort. Which is what you have to do on a single speed. Hub gears have a set of 3 to 14 gears. My hub gear bikes all have 8 gears (Shimano Alfine or Nexus).
Bike with derailleur gears have separate, visible cogs at the rear and often at the cranks too. Look at the right-hand side of the rear wheel of a bike and you will see them. If there is only one "cog" attached to the cranks and 7 "cogs" attached to the rear wheel then you have a 7 speed bike. As there are 7 different gear ratios. If you have, as I do, 3 cogs attached to the cranks and 9 cogs at the rear SOME PEOPLE DESCRIBE THAT AS "27 SPEEDS". Because 9 times 3 is 27. However, that isn't really accurate. Because the various combinations of cogs don't really give 27 discrete, separate ratios between pedalling and road speed. My bike for instance has 9 "speeds" when I'm using the middle crankring (the one attached to the pedals), 2 higher ratios above it for the larger crankring, and 2 lower ratios when I'm using the small crankring. There are many different ratios in the middle, but they overlap. So I have effectively a "13 Speed" bike.
What is slightly more useful to look at is gear "range". Which is the difference between the lowest and the highest gear. Usually expressed as a percentage. On mine I think it is about 530%, which is considered wide.
So comparing gear "speeds" isn't necessarily always what it appears. My nominally "27 speed" derailleur bike has the same gear RANGE as a bike equipped with the "14 speed" Rohloff hub gear system.
My Shimano Alfine hub gear bike has a range of about 300%. I sometimes find that bottom gear isn't low enough (difficult to get up hills) and top gear isn't high enough (I 'spin out' on downhills).
A man called Sheldon Brown (RIP) has a very useful calculator to work these things out:
Though you do need to know what sprockets and chainrings you have on the bike you are looking at to make use of it.